HOUSTON — While Jeremy Lin and the Rockets defeated the Knicks for the fourth straight time on Friday at Toyota Center, Lin's successor, Raymond Felton, continued to speak mysteriously about…

Carmelo Anthony stood in the corner, waving his arms pleading for J.R. Smith to get him the ball. But in the final frantic seconds of a game the Knicks played well enough to win, Anthony simply became the world’s most expensive decoy.

Neither the Knicks nor Stoudemire had previously revealed the news, but Metta World Peace said last week that he had consulted with Stoudemire regarding the use of platelet rich plasma therapy and mentioned that Stoudemire had undergone the procedure himself.

Pau Gasol had 23 points and 17 rebounds, and the injury-riddled Los Angeles Lakers used their sixth different starting point guard of the season Friday night in a 110-99 victory over the Utah Jazz.

Jan 3 (Reuters – Los Angeles Clippers point guard Chris Paul could be sidelined for up to five weeks after suffering a separated right shoulder in Friday’s 119-112 win over the Dallas Mavericks.

The Cavaliers’ All-Star guard, Kyrie Irving, will miss Saturday’s game against the Nets with a bruised left knee. He also sat out Thursday’s home win over Orlando.

DeAndre Jordan and Blake Griffin found a way to win without Chris Paul.

The chairwoman of the Los Angeles Sparks, Paula Madison, has told the W.N.B.A. that the league should look for new owners of the club.

Compiling a season-high 29 assists, with 11 by Kyle Lowry, and getting 17 or more points from four players, including 20 from DeMar DeRozan, the Raptors beat the Wizards.

One night after a stirring victory in San Antonio, the Knicks lost in the final seconds, in part because of an ill-advised shot by J. R. Smith.

Ty Lawson scored 18 points, including a key 3-pointer with less than a minute to play, and the Denver Nuggets snapped an eight-game losing streak with a 111-108 win over the Memphis Grizzlies on Friday night.

Los Angeles Clippers guard Chris Paul will miss three to five weeks after separating his right shoulder in a game against Dallas.

James Harden scored 37 points and Aaron Brooks made a pair of free throws with 17 seconds left to lift the Houston Rockets to a 102-100 win over the New York Knicks on Friday night.

The Nets followed up a big loss to the Spurs with a stirring victory against the Thunder, just as they did last season to start a seven-game winning streak.

Iman Shumpert, often dejected during the first two months of the season, had a renewed confidence after scoring 27 points Thursday. He added 26 points Friday.

Andre Iguodala hit a 3-pointer at the buzzer, David Lee scored 23 points and the Golden State Warriors won their eighth straight game with a 101-100 victory over the Atlanta Hawks on Friday night.

Anthony Davis had 23 points and nine rebounds and Tyreke Evans scored 16 points with a key basket late to lead the New Orleans Pelicans to a 95-92 win over the Boston Celtics on Friday night.

DeMar DeRozan scored 20 points, Kyle Lowry outplayed John Wall with 19 points and 11 assists, and the Toronto Raptors won their season-high fifth consecutive game by beating the Washington Wizards 101-88 Friday night.

I recently took a 10 year old kid to his first basketball game. Great game. The home team calls timeout with 1 second left down two. The coach is frantically drawing up a play. The gym is rocking. Everyone is on their feet screaming. The cheerleaders are biting their nails. The mascot has his eyes covered. My sons are nervously hugging each other. The kid gets this puzzled look on his face and turns to me and asks, “What’s the situation?” I almost burst out laughing. I think to myself, “How in the world do you not know ‘the situation’?” So, I calmly explain to him, “You see JR, this is ‘the situation’…” Yeesh…

Did ruruland just say that at another point in J.R.’s career, that would have been a good shot for the Knicks?

I don’t care if he’s a 50% 3PT shooter. That is a bad play.

Also, Richard Jefferson is now a “trade target” for the Cavs and the Clippers are thinking about trading Blake Griffin for Carmelo Anthony.

How many idiots are left in NBA front offices?

It’s fun to blame JR and make believe the knicks would have won this game if he didn’t take that shot.

Alternative Reality: Knicks hold for last shot. Melo misses 15 foot, double teamed, iso fade-away. knicks lose in OT.

While it would be kind of poetic for the next worst owner in the league to rescue the Knicks from the worst owner in the league with a Melo-Blake trade, I can’t imagine we’re that lucky.

But isn’t it pretty to think so?

Did ruruland just say that at another point in J.R.’s career, that would have been a good shot for the Knicks?I don’t care if he’s a 50% 3PT shooter. That is a bad play.Nope. Life is complicated. Let’s say JR was a 50% 3pt shooter per your assumption. That shot, an assisted, uncontested, on-balance 3 is far more efficient than an average 3, and he would be even better than 50%. But let’s just use your 50% as the number on that particular shot instead. He took the shot with 21 seconds left. He has a 50% chance of giving the Knicks a 1 point lead with about 19 seconds left.

A generic NBA team down by 2 with the ball, a full shot clock, and 21 seconds left (i.e. the Knicks when JR shot) has roughly a 24% chance to win the game. This is an unconditional win probability, meaning it uses actual strategies employed (i.e. which predominantly has meant trying to hold for the last shot) over the last decade. If JR makes the shot, then the Rockets have the ball with around 19 seconds left and a 1 point deficit. A team in this situation will win around 39% of the time. So JR making the shot takes the Knicks WP from 24% to 61%. If JR misses, the Knicks get the OR ~30% of the time and maintain their 24% win probability. If they don’t, they still have an 9% chance to win. So:

JR Make: 0.5 X (.61 – .24) = .185

JR Miss: 0.5 X 0.3 X .24 = .036

JR Miss: 0.5 X 0.7 X .09 = .032

Total = .253

So if JR Smith has a 50% chance of making that 3, the shot is slightly beneficial to the Knicks. In fact, because the Knicks are the underdog, the probability tilts even further toward shooting. This is because the underdog wants to increase risk and decrease the chance of overtime. Remember, holding for one shot often requires a choice between a very difficult shot or still leaving time for Houston. Obviously, JR did this math before shooting but doesn’t want to blow his Twitter cred.

Them were some nice maths there, but the score was tied, so your calculations: they do nothing.

Barring a non-shot turnover, the Rockets had a 0% chance of winning the game in regulation had the Knicks held the ball until shooting at the buzzer. With a FG% of even 35 at that point (because eFG% doesn’t matter in that situation, as any score wins the game), the Knicks have an enormous advantage. It was a bad play.

And by enormous advantage I mean “the Rockets cannot win the game in regulation unless the Knicks turn the ball over or leave time on the clock after their final FGA,” which is pretty fucking huge.

Them were some nice maths there, but the score was tied, so your calculations: they do nothing.I’m Sorry — I did both the JR’s-wrong-score version (NYK down by two) and the actual game version. But in the actual game version (tied), the shot is also easily the right move if he is 50% to make. A team tied with 21 seconds to go and possession wins 60.5% of the time. If the ball goes in, the Knicks lead by 3 with 19 seconds but Houston has the ball: NYK are an 87.4% favorite. If the Knicks get the OR, their win probability is unchanged. If Houston gets the DR, they have the 60.5% chance to win. The math:

Make: 0.5 X 87.4 = 0.437

Miss and ORB: 0.5 X .3 X 60.5 = 0.0908

Miss and DRB: 0.5 X .7 X 39.5 = 0.138

Total = 66.6

So shooting takes the Knicks’ win probability from 60.5% to 66.6%. And the previous point I made about the Knicks being the underdog (if you believe that) in overtime applies even more strongly here and makes the shot even more efficient. As it stood, JR was probably correct to shoot even in real life. It works even if JR is 40% to make that shot, which is very low for an uncontested, on-balance 24 footer.

[Note the above example includes a mistake in the first line; it should simply read .5 X .61 = .305. The shot is a no-brainer if down by 2: 37% WP versus existing 24% WP.]

That is huge, but Hello-Hello-you play to win the game. You play to win the game. At some point JR shooting is the best option, because even though the Rockets cannot win the game in regulation they can win in overtime if we don’t score on our last possession.

Agree with Jowles completely, holding the ball for a final shot is truly a no-brainer if there ever was one. If we are down 2, it’s a decent shot. If down 3, it’s a no-brainer to take it. NBA basketball 101 stuff.

That’s true, but even if you have J.R. close his eyes and chuck a shot with 20% chance to go in, the Rockets have a 0% chance of winning in regulation if they are not allowed to touch the basketball.

And if they go to OT, the Knicks might still have a 40% chance of winning through simple team efficiency metrics, even as a bad team.

You comprehended none of that, Jowles.

Nice job, ptmilo.

I think it’s fair to say that the actual loss of equity in JR taking the shot is probably not as extreme as some might suppose, given the apparent stupidity of him not knowing the score.

But I also find the math puzzling, especially the assumption that JR is 50% to hit that three. Does that win probability chart control for the shot clock or the fact the Rockets were in the penalty?

IMO, the idea that JR Smith was 50% on that last shot is pure fantasy.

1. The league average for 3s is about 35% (give or take). JR Smith shot a straightaway 3. Those are the lower probability 3s. It’s the corner 3s where some real damage can be done.

2. JR Smith has been a slightly below average shooter this year.

3. JR Smith was 1 for 7 and 3 for 12 overall shooting on the night.

4. It was a game deciding shot. Even though I haven’t seen the stats, I’m going to comfortably guess that the success rate is lower under high pressure.

This is the non math thinking.

The probability of either team winning in OT is almost irrelevant. No matter how you get to OT, the probability of winning the game stays the same. The only probability that is relevant is the Knicks chances of winning in regulation.

Ideally their best chance of winning is to ensure they take the last shot with 1 second left and it’s a dunk/layup. That way they would almost always win, very rarely go into overtime, and never lose in regulation. There would be no cost to missing. After that, there’s a kind of curve where you are weighing the probability of making the shot vs. the cost of giving the other team a chance to tie or win in regulation. The closer you get to zero seconds left the better and the easier the shot the better.

The detailed math is beyond me because there are too many combinations, but a straightaway 3 pointer from JR with 17 seconds left is so beyond obviously wrong, I can’t believe it is even being debated. There was plenty of time to get off an equal or possibly even higher probability shot and simultaneously reduce the chances of the opponent scoring by leaving less time on the clock. Even if they didn’t get off an equal or better shot, the reduction of time by waiting would be adding equity as long as they got off any reasonable shot. This was clearly too soon for that shot.

That’s true, but even if you have J.R. close his eyes and chuck a shot with 20% chance to go in, the Rockets have a 0% chance of winning in regulation if they are not allowed to touch the basketball.And if they go to OT, the Knicks might still have a 40% chance of winning through simple team efficiency metrics, even as a bad team.If the probabilities seem to defy common sense, let me try to help with the intuition.

In your example, the hold-for-one strategy only gives the Knicks 52% chance to win (the easy math is ((.2 * 1) + (.8 * .4)). That would be far wrose than the WP from JR shooting the 3 using any plausible assumptions. But since your example was meant as random hyperbole, let me try to help with the intuition; it’s hard to convince people with math unless you’re also willing to be obscurantist like some popular NBA acronym hawkers.

One key intuition is that it is not easy to effectively hold for one shot. Some attempts to hold for one shot result in a difficult shot that still leaves time for the opponent to call time out & hoist a similar shot. Others result in no shot at all (sometimes even a turnover or offensive foul). And as you noted, even perfectly timed attempts tend to be very low % shots. This is why a team only has a 60.5% chance to win the game when they have the ball with 21 seconds left of a time game (even lower if you assume they were an overtime underdog like the Knicks).

Considering that the Knicks were in fact not the favorite to win in OT, there is no reasonably argument that this was a terrible play. Even if JR was only 35% on that shot and the Knicks were 50/50 in OT, the shot is neutral (i.e. 60.4% WP). Neither of those assumptions are fair- most studies show that open, assisted 3s add 10%+ to 3pt efficiency, and the Knicks were underdogs.. The conclusion (that will probably die shivering alone in this thread) is this was very probably the right take and cannot reasonably be called a terrible play.

The probability of either team winning in OT is almost irrelevant. No matter how you get to OT, the probability of winning the game stays the same. The only probability that is relevant is the Knicks chances of winning in regulation.No, you have to think harder about this. Some outcomes reduce the chance of overtime and thus favor the underdog, if there is an underdog. Taking a 3 here absolute reduces the chance of overtime versus holding for 1. For that reason, both expected values and distributions matter.

4. It was a game deciding shot. Even though I haven’t seen the stats, I’m going to comfortably guess that the success rate is lower under high pressure.Game deciding shots are far lower efficiency because they are more contested, less assisted, and less on-balance. Most of the evidence seems to show that game deciding open, assisted shots are similar to normal open, assisted shots. And open, assisted shots are very different than contested shots at all times.

Incidentally the best public win probability calculator for the NBA that I know of is here:

http://stats.inpredictable.com/nba/wpCalc.php

2. JR Smith has been a slightly below average shooter this year.By the way, I’m guessing you’d be surprised to know JR is shooting 37% this year on 3s not taken from the corner or beyond 30 feet (11 so far).

PTMilo – You sound like you have access to more granular data. What’s the difference in win expectancy between having the ball with 19 seconds and the shot clock off and having it expiring?

It would seem to me that a win probability chart that doesn’t take the shot clock into account is kind of useless? I could be wrong though….

PTMilo – You sound like you have access to more granular data. What’s the difference in win expectancy between having the ball with 19 seconds and the shot clock off and having it expiring?It would seem to me that a win probability chart that doesn’t take the shot clock into account is kind of useless? I could be wrong though….No, you’re right, it does seem like it should matter. And I don’t have a way to easily answer this question. But as I just said on the other thread, one fact that stares you in the face is that WP only drops from 60.5% to 59.4% if you change the time remaining from 21 to 32 seconds (eliminating the hold for one option) for the team with the ball. This seems to suggest that the hold-for-one option is not driving the car here. Also note that if you drop the time remaining to 6 seconds, making shot clock problems less likely but leaving time to run a play, the WP actually drops to 59.8%.

PTMilo – I appreciate your making the case. It’s a knickerbloggian thought, though academic in some sense given the fact that JR didn’t know the score.

I don’t think there is a case that JR shooting there was a dominant strategy relative to shooting later in the clock and with a higher percentage approach. The assumption that his was the best shot they were likely to get seems to be incorrect. Working the clock down below five seconds and taking a quality 2 or trying to draw a foul seems to have significantly higher win expectancy.

But as I said upthread, I could be convinced that the equities involved are probably not what people imagine.

One thing I would note, I don’t agree with Stratomatic that the overtime odds are irrelevant. The Rockets are a lot better than the Knicks and playing at home is also a small additional advantage. Their odds of winning in overtime were probably 70% if you give Vegas lines any credence. (Rockets went off as 11.5 point favorites)

So ending the game in regulation was hugely to the Knicks advantage. I just don’t agree that they went about it in anything close to the optimal way.